    The examples and discussions presented in §REF  indicate that the graph polynomial approach we formulate is capable of tracking the changes in topology of the embedded graph upon carrying out certain transformations that are discussed in §. As discussed there, this is of likely relevance to the study of dynamical transitions in non-linear dynamical systems [1]}, [2]} and phase transitions in statistical mechanics within the Ginzburg-Landau-Wilson paradigm [3]}. Our formalism is likely to be relevant to the paradigm of fermionic criticality, i.e., the Lifshitz phase transitions of systems of interacting fermions that involve changes in the topology of the Fermi volume [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}.
